An algorithm for detecting a change in a stochastic process

Bansal, Rajeev; Papantoni-Kazakos, P.

doi:10.1109/tit.1986.1057160

Cited by 89 publications

(26 citation statements)

References 15 publications

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“…The study of the CUSUM rule convergence properties has been the subject of an extensive literature for fifty years. Among the most striking results, the works of Lorden [19] or Moustakides [24] can be mentioned in an independent and identically distributed (iid) context and Bansal and Papantoni-Kazakos [2], Lai [16], Fuh [9] or Mei [22] treat the case of dependent data.…”

Section: Introductionmentioning

confidence: 99%

Change detection for uncertain autoregressive dynamic models through nonparametric estimation

Hilgert

Verdier

Vila

2016

Statistical Methodology

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A new statistical approach for on-line change detection in uncertain dynamic system is proposed. In change detection problem, the distribution of a sequence of observations can change at some unknown instant. The goal is to detect this change, for example a parameter change, as quickly as possible with a minimal risk of false detection. In this paper, the observations come from an uncertain system modeled by an autoregressive model containing an unknown functional component. The popular Page's CUSUM rule is not applicable anymore since it requires the full knowledge of the model. A new detection CUSUM-like scheme is proposed, which is based on the nonparametric estimation of the unknown component from a learning sample. Moreover, the estimation procedure can be updated on line which ensures a better detection, especially at the beginning of the monitoring procedure. Simulation trials were performed on a model describing a water treatment process and show the interest of this new procedure with respect to the classic CUSUM rule.

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Section: Introductionmentioning

confidence: 99%

Change detection for uncertain autoregressive dynamic models through nonparametric estimation

Hilgert

Verdier

Vila

2016

Statistical Methodology

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“…(Lorden 1971) analyzed Page's algorithm and proved its asymptotic optimality in the sense of stopping time. (Bansal et al 1986) extended Page's algorithm for stationary and ergodic processes with memory and proved optimality in the sense of asymptotic expected stopping time. (Bansal et al 1989) also "robustified" the algorithm for resistance to data outliers.…”

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confidence: 99%

“…(Bansal et al 1989) also "robustified" the algorithm for resistance to data outliers. extended the algorithm in (Bansal et al 1986) to sequentially detect reoccurring possible changes within a given set of stochastic processes, and analyzed asymptotic performance. (Lai 1995) considered a scenario similar to that in .…”

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confidence: 99%

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Monitoring Changes in Operational Scenarios via Data Fusion in Sensor Networks

Papantoni-Kazakos¹,

Titsa²,

Burrell³

et al. 2009

Sensor and Data Fusion

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“…By the contributions of earlier works of Shiryayev [21], Lorden [14], Bansal [3], and Tartakovsky [23], [24] this procedure could be said optimal (at least asymptotically optimal), in the sense that it minimizes the detection delay for a fixed false alarm probability.…”

Section: Introductionmentioning

confidence: 99%

The minimal time detection algorithm

Kim¹

Proceedings of 1994 IEEE Aerospace Applications Conference Proceedings

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-An aerospace vehicle may operate throughout a wide range of flight environmental conditions that affect its dynamic characteristics. Even when the control design incorporates a degree of robustness, system parameters may drift enough to cause its performance to degrade below an acceptable level. The object of this paper is to develop a change detection algorithm so that we can build a highly adaptive control system applicable to aircraft systems. The idea is to detect system changes with minimal time delay. The algorithm developed is called Minimal Time-Change Detection Algorithm(MT-CDA) which detects the instant of change as quickly as possible with false-alarm probability below a certain specified level. Simulation results for the aircraft lateral motion with a known or unknown change in control gain matrices, in the presence of doublet input, indicate that the algorithm works fairly well as theory indicates though there is a difficulty in deciding the exact amount of change in some situations. One of MT-CDA distinguishing properties is that detection delay of MT-CDA is superior to that of Whiteness Test.

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An algorithm for detecting a change in a stochastic process

Cited by 89 publications

References 15 publications

Change detection for uncertain autoregressive dynamic models through nonparametric estimation

Change detection for uncertain autoregressive dynamic models through nonparametric estimation

Monitoring Changes in Operational Scenarios via Data Fusion in Sensor Networks

The minimal time detection algorithm

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